I assume the green pipe with green cement cap is a large diameter like 18" to 24". That is the access to the septic tank for inspection and pumping. Older installations have one and newer installations have two.

The white PVC pipes are about 4" diameter? If they are far away from the cement cap then they are inspection access to the two runs of the leach field. You can repair that by cutting the pipe straight and using a section of PVC that has a female at one end. Glue to the stub you have and cut at the desired height and slip on (don't glue) a cap. You can also use a twin female coupling and another piece of 4" PVC but the first solution is more sano. You can dig down and cut the pipe below grade so you never see the repair. you can raise both pipes a couple feet above grade so you don't mow them again.

When you bought your house there should have been a septic inspection and pumping. You should have been there for that. You can call a local septic pumping company and ask them to come out and give you the septic 101 and arrange for routine pumping at whatever year intervals they suggest.

You should start by getting a copy of your permit from the county health department.

Other than that, is it a gravity system, a pump system and if so pump to gravity or prssurized dispersal? Your permit should tell you those things. Are those pipes over the tanks or over the drainfield?